Lakshmi, the owner of a textile factory in Coimbatore, is strategizing the production for the next quarter. She has to decide on the allocation of three types of fabrics – Cotton, Silk, and Wool – across four different product lines: Shirts, Dresses, Trousers, and Scarves. Each product requires a specific quantity of fabric per unit.

The constraints are:

- The factory has 600 meters each of Cotton and Silk, and 400 meters of Wool.
- Each Shirt requires 2 meters of Cotton, 1 meter of Silk.
- Each Dress needs 3 meters of Silk and 2 meters of Wool.
- Trousers require 2 meters of Cotton and 1 meter of Wool.
- Scarves need 1 meter of Silk and 1 meter of Wool.
- The production targets are 100 Shirts, 80 Dresses, 150 Trousers, and 200 Scarves.

Lakshmi needs to ensure the optimal use of fabric while meeting production targets.

**Questions:**

1. **How much total Cotton is required to meet the production target for Shirts and Trousers?**

A) 500 meters

B) 700 meters

C) 400 meters

D) 600 meters

2. **Is the available Silk sufficient to meet the production targets for all products?**

A) Yes

B) No

C) Only if additional Wool is procured

D) Cannot be determined

3. **If Lakshmi decides to reduce Scarf production by 50 units, how much Wool will be saved?**

A) 50 meters

B) 100 meters

C) 150 meters

D) 200 meters

4. **What is the maximum number of Dresses that can be produced with the available Silk and Wool?**

A) 80

B) 100

C) 120

D) 60

**5. Lakshmi prioritizes meeting the production targets for Shirts and Trousers, how many Scarves can be produced with the remaining fabric?**

A) 100

B) 150

C) 200

D) 250

## Answers

1. Answer: B) 700 meters

Explanation: Shirts require 200 meters of Cotton (100 Shirts × 2 meters each), and Trousers require 300 meters (150 Trousers × 2 meters each). Total Cotton = 200 + 300 = 500 meters.

2. Answer: B) No

Explanation: Silk needed: Shirts = 100 meters, Dresses = 240 meters (80 Dresses × 3 meters each), Scarves = 200 meters. Total = 100 + 240 + 200 = 540 meters, which is less than the available 600 meters.

3. Answer: B) 100 meters

Explanation: Each Scarf needs 1 meter of Wool. Reducing production by 50 units saves 50 meters of Wool.

4. Answer: A) 80

Explanation: Silk limitation: For 80 Dresses, 240 meters of Silk are needed. Wool limitation: For 80 Dresses, 160 meters of Wool are needed. Both are within the available quantity (600 meters of Silk and 400 meters of Wool).

5. Answer: C) 200

Explanation: After allocating for Shirts (200 meters Cotton) and Trousers (300 meters Cotton), no Cotton remains. However, Wool is still available. With the remaining Wool (400 – 150 for Trousers = 250 meters), 200 Scarves can be produced (1 meter Wool each).

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